reserve n,m,k for Nat,
  x,X for set,
  A for Subset of X,
  A1,A2 for SetSequence of X;

theorem Th55:
  (superior_setsequence(A (/\) A1)).n = A /\ (superior_setsequence A1).n
proof
  (superior_setsequence(A (/\) A1)).n = Union ((A (/\) A1) ^\n) by Th2
    .= Union (A (/\) (A1 ^\n)) by Th16
    .= A /\ Union (A1 ^\n) by Th38
    .= A /\ (superior_setsequence A1).n by Th2;
  hence thesis;
end;
